Home HomeChristopher J. Norwood, Defence Science and Technology Organisation (Australia)
Vibration analysis techniques have been used for crack detection for many years. Recently much of the emphasis in this area has been on the use of shifts in natural frequency as an indicator of damage. The vibration response of a structure is determined by the mass and stiffness distribution throughout the structure. In a similar manner the structural intensity or power flow in the structure is determined by the mass, stiffness and damping distributions. This paper examines the effect of a crack on the flexural power flow in a beam. Expressions for the transmission and reflection of flexural waves incident on a crack are derived. A fracture hinge representation of the crack is used and the analysis shows that at the crack there is a discontinuity in the reactive intensity. The size of the discontinuity is dependant upon the crack size and the wave number. Experimental measurements of the power flow in a simulated infinite beam with a crack are made using the wave decomposition method. These results confirm the existence of the discontinuity in the reactive intensity at the crack. The use of wave number measurements as a crack indicator was also tested experimentally and found to be superior to intensity.
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Mogens Ohlrich, Technical University of Denmark (Denmark)
E. Henriksen, Technical University of Denmark (Denmark)
S. Laugesen, Technical University of Denmark (Denmark)
Uncertainties in power measurements performed with piezoelectric accelerometers and force transducers are investigated. It is shown that the inherent structural damping of the transducers is responsible for a bias phase error, which typically is in the order of one degree. Fortunately, such bias errors can be largely compensated for by an absolute calibration of the transducers and inverse filtering that results in very small residual errors. Experimental results of this study indicate that these uncertainties will be in the order of one percent with respect to amplitude and two tenth of a degree for the phase. This implies that input power at a single point can be measured to within one dB in practical structures which possesses some damping. The uncertainty is increased, however, when sums of measured power contributions from more sources are to be minimised, as is the case in active control of vibratory power transmission into structures. This is demonstrated by computer simulations using a theoretical model of a beam structure which is driven by one primary source and two control sources. These simulations reveal the influence of residual errors on power measurements, and the limitations imposed in active control of structural vibration based upon a strategy of power minimisation.
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Jonathan D. Blotter, Idaho State University (U.S.A.)
Gary A. Fleming, NASA Langley Research Center (U.S.A.)
Robert L. West, Virginia Polytechnic Institute & State University (U.S.A.)
Experimental Spatial Power Flow (ESPF) is a non-intrusive spatially continuous laser based technique for extracting the power flow from vibrating strucutres. The ESPF approach retains the spatial representation of the power flow, obtained from analytical models, and represents the actual boundary conditions by using experimental data obtained from a scanning laser Doppler vibrometer. In this paper, ESPF results are compared to the power injected into a simply supported plate which is excited by two shakers placed diagonally across the plate. The two shakers are phased such that one acts as a power source and the other a power sink. The power injected and absorbed by the two shakers is computed from impedance head measurements. Model order convergence capabilities of the power flow computed using the ESPF techniuqe are also demonstrated.
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Hisami Ohishi, Kogakuin University (Japan)
Shinichi Ohno, University of Tokyo (Japan)
Levels of structural vibration reduced by damping treatment can be evaluated by consumption of vibration energy derived from distributions of structural intensity and strain energy. However, it is difficult to estimate accurately structural intensity and strain energy in the structure with damping treatment. In this paper, therefore, we propose a method to estimate more accurately structural intensity and strain energy using the mode shapes which are approximated by superposition of the natural mode shapes of the structure without damping treatment. First, structural intensity and strain energy of the equivalent system of a beam with damping treatment and a damper are calculated by this method, and its accuracy is examined. Then, the effect of damping treatment are discussed based on the distributions of the structural intensity and the strain energy. Finally, validity of this method is examined.
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Toru Yamazaki, University of Tokyo (Japan)
Minoru Kamata, University of Tokyo (Japan)
Shinichi Ohno, University of Tokyo (Japan)
The main purpose of structural intensity measurement is the estimation of power propagating through structures and the detection of excitation position. To accomplish these purposes, the intensity flow is measured at many points on structures by a method based on the finite difference approximation which requires five accelerometers (5-transducer array method). And in the detection of excitation position, the wave decomposition method which reveals the effect of evanescence wave field is employed. Moreover, to estimate the propagating power, the mean power flow is also calculated using the individual wave amplitudes which are obtained from the wave decomposition method. In this report, our approach described above is investigated using a box-like structure. As a result, the propagating power can be determined by the 5-transducer array method or by the calculation of mean power flow within practical error level. And the approach is also applied to analyse the power flow on vehicle body panels. The results indicate that the approach is effective to know the power flow and to estimate the propagating power, and we can say our approach enables us to analyse the power flow in a certain extent precision.
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